Theorems · Theorem · nonassociative algebras
LieSubmodule.map_incl_le
∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [inst_4 : LieRingModule L M] {N : LieSubmodule R L M} {N' : LieSubmodule R L ↥N},
LieSubmodule.map N.incl N' ≤ N- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- le_topproof · cited by 411
- LieSubmodule.mapstatement and proof · cited by 49
- LieSubmodule.inclstatement and proof · cited by 29
- LieSubmodule.map_monoproof · cited by 4
- LieSubmodule.map_incl_topproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.mem_rootSet_invtSubmoduleToLieIdealproof · cited by 2
- LieIdeal.restr_inf_cartan_eq_biSup_corootSubmoduleproof · cited by 1